Biomedical subjects

Daniel B Forger

Publications and source records attributed to Daniel B Forger.

8 recordsLinked to original sources

PubMed2006

Noisy inputs and the induction of on-off switching behavior in a neuronal pacemaker.

Neuronal oscillators can function as bistable toggle switches, flipping between quiescence and rhythmic firing in response to an input stimulus. In theory, such switching should be sensitive to small noisy inputs if the bistable states are in close proximity, which we test here using a perfused squid axon preparation. We find that small noisy stimulus currents induce a multitude of paths between two nearby stable states: repetitive firing and quiescence. The pattern of on-off switching of the pacemaker depends on the intensity, spectral properties, and phase angle of stimulus current fluctuations. Analysis by spike-triggered averaging of the stimulus currents near the transitions reveals that sinusoidal stimuli timed antiphase or in phase with repetitive firing correlates with switching of the pacemaker off or on, respectively. Our results reveal a distinct form of bistability in which noise can either silence pacemaker activity, trigger repetitive firing, or induce sporadic burst patterns similar to those recorded in a variety of normal and pathological neurons.

Algorithms↗

PubMed2006

An opposite role for tau in circadian rhythms revealed by mathematical modeling.

Biological clocks with a period of approximately 24 h (circadian) exist in most organisms and time a variety of functions, including sleep-wake cycles, hormone release, bioluminescence, and core body temperature fluctuations. Much of our understanding of the clock mechanism comes from the identification of specific mutations that affect circadian behavior. A widely studied mutation in casein kinase I (CKI), the CKIepsilon(tau) mutant, has been shown to cause a loss of kinase function in vitro, but it has been difficult to reconcile this loss of function with the current model of circadian clock function. Here we show that mathematical modeling predicts the opposite, that the kinase mutant CKIepsilon(tau) increases kinase activity, and we verify this prediction experimentally. CKIepsilon(tau) is a highly specific gain-of-function mutation that increases the in vivo phosphorylation and degradation of the circadian regulators PER1 and PER2. These findings experimentally validate a mathematical modeling approach to a complex biological function, clarify the role of CKI in the clock, and demonstrate that a specific mutation can be both a gain and a loss of function depending on the substrate.

Animals↗

PubMed2005

Comparison of amplitude recovery dynamics of two limit cycle oscillator models of the human circadian pacemaker.

At an organism level, the mammalian circadian pacemaker is a two-dimensional system. For these two dimensions, phase (relative timing) and amplitude of the circadian pacemaker are commonly used. Both the phase and the amplitude (A) of the human circadian pacemaker can be observed within multiple physiological measures--including plasma cortisol, plasma melatonin, and core body temperature (CBT)--all of which are also used as markers of the circadian system. Although most previous work has concentrated on changes in phase of the circadian system, critically timed light exposure can significantly reduce the amplitude of the pacemaker. The rate at which the amplitude recovers to its equilibrium level after reduction can have physiological significance. Two mathematical models that describe the phase and amplitude dynamics of the pacemaker have been reported. These models are essentially equivalent in predictions of phase and in predictions of amplitude recovery for small changes from an equilibrium value (A = 1), but are markedly different in the prediction of recovery rates when A < 0.6. To determine which dynamic model best describes the amplitude recovery observed in experimental data; both models were fit to CBT data using a maximum likelihood procedure and compared using Akaike's Information Criterion (AIC). For all subjects, the model with the lower recovery rate provided a better fit to data in terms of AIC, supporting evidence that the amplitude recovery of the endogenous pacemaker is slow at low amplitudes. Experiments derived from model predictions are proposed to test the influence of low amplitude recovery on the physiological and neurobehavioral functions.

Biological Clocks↗

PubMed2004

Stochastic simulation of the mammalian circadian clock.

Circadian (nearly 24-h) clocks are remarkably accurate at timing biological events despite the randomness of their biochemical reactions. Here we examine the causes of their immunity to molecular noise in the context of a detailed stochastic mathematical model of the mammalian circadian clock. This stochastic model is a direct generalization of the deterministic mammalian circadian clock model previously developed. A feature of that model is that it completely specifies all molecular reactions, leaving no ambiguity in the formulation of a stochastic version of the model. With parameters based on experimental data concerning clock protein concentrations within a cell, we find accurate circadian rhythms in our model only when promoter interaction occurs on the time scale of seconds. As the model is scaled up by proportionally increasing the numbers of molecules of all species and the reaction rates with the promoter, the observed variability scales as 1/n(0.5), where n is the number of molecules of any species. Our results show that gene duplication increases robustness by providing more promoters with which the transcription factors of the model can interact. Although PER2 mutants were not rhythmic in the deterministic version of this model, they are rhythmic in the stochastic version.

Animals↗

PubMed2004

Model based conjectures on mammalian clock controversies.

We explore some predictions of a previously developed detailed model of molecular timekeeping in mammals (Forger and Peskin, PNAS, 100:14806) in areas where our understanding of clock mechanisms are incomplete. It is conjectured that: (1) the clock's 24-h period depends on mRNA stability. (2) REV-ERBalpha suppresses and/or entrains rhythms in peripheral tissues by regulating CRY1 transcription. (3) CLK:BMAL1 oscillations are suppressed in the suprachiasmatic nuclei to enhance oscillations in other proteins. (4) PER2 is ineffective at causing phase advances because it is not induced by light during the late night. (5) The clock is a limit cycle oscillator that shows characteristics of the evening and morning oscillator model.

Animals↗

PubMed2004

Starting, stopping, and resetting biological oscillators: in search of optimum perturbations.

Biological oscillators are commonly subjected to a single brief stimulus to perturb the ongoing rhythm. After stimulation, the oscillator can recover although its phase may be advanced or delayed relative to the original cycle. A single transient perturbation can also stop the ongoing rhythm. Arthur Winfree systematically classified these responses to brief perturbations, as determined by the strength of the stimulus, and the phase within the cycle at which the stimulus was given. A natural question arises from Winfree's work. Are certain stimulus shapes better than others at achieving a desired effect? The present study explores this question using: (1) analysis of phase space geometry, (2) calculus of variations, and (3) analysis of responses to noisy perturbations. Methods 1 and 2 can yield exact solutions, but have limited applicability in biology because they require a detailed mathematical description of the oscillator. Method 3 is applicable to any oscillator without mathematical prerequisites. We validate this method by finding optimum stimuli that start and stop repetitive firing in a neural pacemaker model, and the optimum light stimulus for resetting the circadian rhythm in a model of the human circadian clock. We propose that the elucidation of optimum stimulus shapes may be useful for studying many periodic phenomena in biology and medicine. Optimum stimuli can be used to induce a desired behavior without producing undesirable side effects.

Biological Clocks↗

PubMed2003

A detailed predictive model of the mammalian circadian clock.

Experimental data on the circadian (approximately 24-h) clock in mammalian cells are vast, diverse, and detailed. Mathematical models are therefore needed to piece these data together and to study overall clock behavior. Previous models have focused on Neurospora or Drosophila or can be converted to a Drosophila model simply by renaming variables. Those models used Hill-type terms for transcription regulation and Michaelis-Menten type or delay terms for posttranslation regulation. Recent mammalian experimental data call into question some of the assumptions in these approaches. Moreover, gene duplication has led to more proteins in the mammalian system than in lower organisms. Here we develop a detailed distinctly mammalian model by using mass action kinetics. Parameters for our model are found from experimental data by using a coordinate search method. The model accurately predicts the phase of entrainment, amplitude of oscillation, and shape of time profiles of clock mRNAs and proteins and is also robust to parameter changes and mutations.

Animals↗

PubMed2003

Development and validation of computational models for mammalian circadian oscillators.

Circadian rhythms are endogenous rhythms with a cycle length of approximately 24 h. Rhythmic production of specific proteins within pacemaker structures is the basis for these physiological and behavioral rhythms. Prior work on mathematical modeling of molecular circadian oscillators has focused on the fruit fly, Drosophila melanogaster. Recently, great advances have been made in our understanding of the molecular basis of circadian rhythms in mammals. Mathematical models of the mammalian circadian oscillator are needed to piece together diverse data, predict experimental results, and help us understand the clock as a whole. Our objectives are to develop mathematical models of the mammalian circadian oscillator, generate and test predictions from these models, gather information on the parameters needed for model development, integrate the molecular model with an existing model of the influence of light and rhythmicity on human performance, and make models available in BioSpice so that they can be easily used by the general community. Two new mammalian models have been developed, and experimental data are summarized. These studies have the potential to lead to new strategies for resetting the circadian clock. Manipulations of the circadian clock can be used to optimize performance by promoting alertness and physiological synchronization.

Animals↗